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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 124950fn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.fy2 | 124950fn1 | \([1, 1, 1, 99812, -14449219]\) | \(59822347031/83966400\) | \(-154352546775000000\) | \([2]\) | \(1327104\) | \(1.9838\) | \(\Gamma_0(N)\)-optimal |
124950.fy1 | 124950fn2 | \([1, 1, 1, -635188, -143809219]\) | \(15417797707369/4080067320\) | \(7500247502041875000\) | \([2]\) | \(2654208\) | \(2.3304\) |
Rank
sage: E.rank()
The elliptic curves in class 124950fn have rank \(0\).
Complex multiplication
The elliptic curves in class 124950fn do not have complex multiplication.Modular form 124950.2.a.fn
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.